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Browsing Mathematics by Issue Date

Browsing Mathematics by Issue Date

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  • Banerjee, Sayan (2014-02-24)
    This dissertation deals with three problems in Stochastic Analysis which broadly involve interactions, either between particles (Chapters 1 and 2), or between particles and the boundary of a C2 domain (Chapter 3). In Chapter ...
  • Wang, Dake (2014-02-24)
    In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1]. In subcritical phases, we construct singular ...
  • Huynh, Anh Trung (2014-02-24)
    This paper reviews the current state of the Lam-Williams conjectures on a multivariate Markov chain on the symmetric group S_n. We start with Lam's work on random core partitions which led to a remarkable Markov chain on ...
  • Taylor, Jair Patrick (2014-02-24)
    We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials. We describe how such a series can be computed by ...
  • Fan, Wai Tong
    This thesis studies the <italic>hydrodynamic limit</italic> and the <italic>fluctuation limit</italic> for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive ...
  • Ward, Matthew J
    This thesis develops a theory of arithmetic Fourier-Mukai transforms in order to obtain results about equivalences between the derived category of Calabi-Yau varieties over non-algebraically closed fields. We obtain answers ...
  • Drugan, Gregory
    We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows ...
  • Deines, Alyson Laurene
    A crowning achievement of Number theory in the 20th century is a theorem of Wiles which states that for an elliptic curve E over <bold>Q</bold> of conductor N, there is a non-constant map from the modular curve of level N ...
  • Slivken, Erik Dustin
    In this thesis we present three problems. The first problem is to find a good description of the number of fixed points of a 231-avoiding permutation. We use a bijection from Dyck paths to 231-avoiding permutations that ...
  • Sisodia, Gautam
    Let <italic>k</italic> be a field and <italic>B</italic> either a finitely generated free <italic>k</italic>-algebra, or a regular <italic>k</italic>-algebra of global dimension two with at least three generators, generated ...
  • Roberts, Austin
    In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's ...
  • Johnson, Tobias Lee
    One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are <italic>universal</italic>. We probe the edges of universality by studying ...
  • Lou, Shuwen
    In this thesis we introduce and study Brownian motion with or without drift on state spaces with varying dimension. Starting with a concrete such state space that is the plane with an infinite pole on it, we construct a ...
  • Tran, Huy Vo
    The Loewner differential equation, a classical tool that has attracted recent attention due to Schramm-Loewner evolution (SLE), provides a unique way of encoding a simple 2-dimensional curve into a continuous 1-dimensional ...
  • Wang, Xingting
    We classify all connected Hopf algebras up to p^3 dimension over an algebraically closed field of characteristic p>0 under the mild restriction such that in dimension p^3, we only work over odd primes p when the primitive ...
  • Lewis, Stephen
    In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space ...
  • Barnes, Joel
    A conformally balanced tree is an embedding of a given planar map into the plane with constraints on the harmonic measure of its edges such that the resulting set is unique up to scale and rotation. Bishop (2013) showed ...
  • Yang, Yang
    Inverse problems arise in various areas of science and engineering including medical imaging, computer vision, geophysics, solid mechanics, astronomy, and so forth. A wide range of these problems involve elliptic operators. ...
  • Pawlowski, Brendan
    A fundamental invariant of a permutation is its inversion set, or diagram. Natural machinery in the representation theory of symmetric groups produces a symmetric function from any finite subset of <bold>N</bold><super>2</super>, ...
  • Erickson, Lindsay
    Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the ...

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